Question

An experiment consists of tossing a fair die until 2 occurs 7 times. What is the probability that the process ends after exactly ten tosses with 2 occurring on the ninth and tenth tosses? (Round your answer to four decimal places.)

Answer 1

0.0004

Explanation:

A fair die has 6 faces.

The probability of obtaining a 2
`=(1)/(6)`

The probability of a number other than 2
`=(5)/(6)`

The experiment consists of tossing a fair die until 2 occurs 7 times.

Therefore, the probability that the process ends after exactly ten tosses with 2 occurring on the ninth and tenth tosses

`=^(10)C_4 * \left((5)/(6)\right)^3 * \left((1)/(6)\right)^7\\\\=0.00043412701 \\ \approx 0.0004 $(correct to 4 decimal places)`